Biostatistical research is proposed to address several methodological problems that arise from mental health epidemiologists' need to obtain reliable and efficient data about the rates of mental disorders in the general community. The problems come from all three phases of epidemiologic research in psychiatry: the establishment of diagnostic reliability, the design of prevalence surveys, and the statistical analysis of multivariate data. The specific aims are:, 1. To develop methods for estimating kappa and its standard error, and for constructing confidence bounds using an efficient test-retest design in which inclusion in the retest phases is dependent on the outcome of the first test. 2. To develop rules for selecting cases for diagnostic validity studies based on two or more independent diagnoses when a single diagnosis has poor predictive power. Unlike previously developed rules, these will not assume that diagnostic sensitivity is constant across all types of patients. 3. To evaluate the efficiency of various designs for two-phase surveys of rare mental disorders. Special attention will be given to designs that employ multivariate screening rules, especially ones that attempt to screen persons for different psychiatric disorders. 4. To develop methods for estimating the standard error of prevalence estimates derived from two-phase surveys, and for constructing confidence bounds around these prevalence estimates. 5. To examine critically the effects mis-specifying a logistic regression model by including independent variables that are not structurally related to the odds of a given outcome. If such effects are nontrivial, to develop practical rules to guide data analysts in logistic model specification. Finally, 6. To investigate the usefulness of permutation tests to evaluate multivariate hypotheses when the multivariate outcome is not multivariate normal. A FORTRAN computer program will be developed to implement multivariate permutation tests, and the results of this method will be evaluated relative to other robust methods. No new data will be collected in the proposed research. Data from surveys of mental retardation and childhood disability will be used to illustrate the methods developed in aims 3 and 4, and data from a case-control study of psychosocial risk factors for depression will be used to illustrate methods developed in aims 5 and 6.